Abstract
Characterization of microelectromechanical systems, MEMS structures is important for their reliability, specifically for life-sustaining applications. Due to size effect, testing must be done at microscale under the same conditions the components are utilized. Microtesting systems have been developed and used for metallic and nonmetallic MEMS components. Other methods including on-the-chip characterization have been developed and utilized. Details of development or utilization of various micro-characterization techniques are presented in this chapter. There are many issues related to mechanical properties, some of which are briefly described here. Modeling MEMS both computationally and mathematically are depicted along with examples. At the end, future trends in MEMS are discussed.
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1 Introduction
Microelectromechanical systems, MEMS devices are becoming ubiquitous, from automotive tire pressure sensors, inertial measurement units, and fuel injection nozzles to aerospace exploration devices. Other applications include tablets, mobile phones and watches, sport wearable gadgets, CO2 and other gas sensors, and even blood viscosity measuring devices. In the light of these facts, special attention must be paid to MEMS characterization. Since mechanical properties are affected by a component’s size, it is important to conduct characterization experiments at a comparable scale. The reliability of MEMS structures becomes vital for applications where human life is at stake. Examples are triggers for airbags and weaponry, life-supporting medical devices, and navigating systems for airplanes and vehicles. While macroscale mechanical characterization is well established, the processes at microscale yet have to be developed, enhanced, and standardized. Since MEMS field is relatively new, researchers are still trying to find more effective ways to characterize and model the behavior of MEMS structures.
To design, fabricate and successfully test MEMS components, an integrated approach is needed that provides Analysis, Computational and Experimental Solution(s) (ACES) [1]. This methodology employs analytical tools that are based on exact closed form solutions. Commonly used computation methods such as finite element method, FEM, boundary element method, BEM, and finite difference method, FDM, treat problems numerically, and provide approximate solutions. The degree of approximation, however, depends on the characteristics of the differential equations and the specifications of the boundary, initial and loading (BIL) conditions [1]. Unlike analytical or computational methods, experimental tools examine and evaluate actual objects, their performance, and their respective operating conditions and offer characteristics for those objects. The successful design and development of MEMS, with added complexity due to size effect, requires a combination of both experimental and theoretical tools [1].
2 Mechanical Properties-Related Issues
The movement of the mechanical components of MEMS is often associated with loads that can cause fatigue and failure of the systems. Mechanical properties such as strength, toughness, and fatigue life become important for the safe operation of MEMS. Devices such as micromirrors potentially have millions of mechanical components that tilt at high frequencies. Stresses developed in the hinges can lead to premature failure of one of these, possibly rendering the whole device useless. For bioMEMS that deal with various fluids, aggressive environments can lead to stress corrosion cracking. High-aspect-ratio surface-machined BioMEMS components such as microneedles and thermal-post heat-exchangers require good fracture toughness in addition to reasonable strength. Microengine components rely on good tribological properties. Adhesion properties of MEMS are important for microswitches. Thermal actuators operate at higher temperatures and therefore need good thermal-fatigue as well as creep resistance.
The effect of size on mechanical properties is well known for small structures. While elasticity modulus is not size-dependent (for same crystal orientations), other properties such as strength, fatigue limits, fatigue life, and hardness are size dependent. The effect becomes more pronounced when the size of the structure approaches the order of the grain size. Grain growth is one of the factors that affects the strength of the MEMS structures. Consider LIGA MEMS components being grown in PMMA molds. Initially, grains are very fine. This means a thin film, with a microstructure mostly made of these fine grains, will be pretty strong. This is not the case for thicker films where the fine grains were allowed to grow into coarse columnar grains, subsequently reducing the overall strength of the film. Such reduction in strength as well as in fatigue limit is well documented [2]. This is the case for most thin film depositions, lithography-based electrodepositions, and other additive processes.
Environmental effects on silicon greatly influences the reliability of MEMS devices. Stiction, specifically for MEMS moving components is one of the major failure causes. This happens to sliding surfaces that stick to each other during motion [3]. Presence of water vapor, not only promotes stiction, but also causes, fatigue damage accumulation [4] as well as stress corrosion cracking [5–7]. Stress-assisted dissolution of silica backbone at loci of high stresses (e.g., at the notch root) is postulated to be the mechanism for deepening the surface perturbations, leading to the formation of the grooves [4, 8–10]. Another mechanism for crack initiation has been suggested to be the thickening of the native silicon dioxide layer at locations where stress levels are high. Cracks have been suggested to start from these thick silicon dioxide regions [5].
Failure analysis of MEMS structures has been performed by optical and electron microscopy, atomic force microscopy, acoustic microscopy, focused ion beam microscopy, and scanning laser microscopy. It has been hard to duplicate failures in MEMS. This has been a major challenge in the failure analysis of these systems [11]. Reliability studies on silicon MEMS include the electrical actuation of comb drives. However, there are other characterization tools, such as in situ visual inspection of moving components, acquiring test data and tools for obtaining performance characteristics [12]. A number of reliability factors have been studied for silicon. These are frequency [13], shock resistance [14, 15], stiction [16], mechanical wear [17], fatigue [18, 19], fracture [20], vibration [21], and environmental effects [22]. MEMS devices that have been studied include microactuators [12, 23], microengines [13, 24], microrelays [25], thin films [26, 27], and resonating structures [6, 7] among others.
MEMS mechanical reliability studies have been conducted for decades [28, 29]. However, there are still many MEMS applications that are not possible because of the lack of mechanical behavior characteristics of such systems [30]. Although analytical models have been developed [31–35] to predict the reliability of MEMS or to help with reliability design rules, nevertheless, mechanical tests are still needed to provide data that validate such predictions.
Actuation of MEMS is achieved by different methods. Conventional approaches are simple and easy to implement and integrate into the circuits. There are still challenges associated with each of these methods. Electrostatically driven actuators are one-dimensional and effective. Examples are comb drives with interdigitating combs that can be used for both actuation and sensing. The main challenge is the high voltages (tens if not hundreds of volts) required for their actuation [36]. On the other hand, magnetically driven actuators use smaller voltages but higher currents that make them ineffective as thin films [37]. Despite their high energy densities, it is difficult to integrate them with conventional semiconductor processing techniques. When it comes to efficient actuators such as piezoelectrics, the challenge lies in their design for in-plane movement [38]. While yielding high forces, thermal actuators generate small displacements. Nevertheless for large displacements, they yield small forces making these actuators ineffective [39]. Efforts have been made to mitigate this problem by fabrication of a thermal actuator with medium range forces associated with medium range displacement [39]. In this design, two thermal actuators generate rotation deflections that cause the motion of a cantilever at a voltage of 13.3 V and a current of 39 mA. The cantilever has a spring constant of 65.5 N/m and can deliver noticeable forces. Deflections of up to 28 μm and force efficiencies of up to 7 mW/μN have been reported [39].
3 Microtesting Systems
Microtensile Testing: The pioneering work of Sharpe and McAleavey [40] in developing microtensile and microfatigue testing systems was continued by other researchers who complemented these systems with new measurement techniques. Figure 7.1 presents the schematic of an early system that utilizes laser interferometry in measuring displacement.
The microtensile testing system utilizes various types of microsamples. One such microspecimen is a small dog-bone shape structure made of LIGA Ni MEMS deposited in PMMA molds. This structure has triangular ends, and its gage section measures 200 μm × 200 μm × 400–1000 μm. Both sides of the samples are polished to a mirror finish, and then marked in two locations by a pyramid indenter. These inverted pyramid indents are necessary for reflecting a laser beam leading to interferometry patters. Samples are mounted on small holders that are attached on one side to a fixed mount and on the other to the piston of an air bearing. The latter is part of a load train that connects the air bearing to a load cell and to a Uni-slide drive mechanism as shown in Fig. 7.1. The laser beam shines on the two inverted pyramids and generates reflected beams that interact and form interferometry patterns. These patterns are projected onto two photodiode arrays (detectors) mounted on two posts at the sides of the laser beam source. Light and dark bands of the pattern are analyzed and the change in fringes is recorded and used in the calculation of strain during tensile testing of the sample. The load cell records the load as the Uni-slide drive imposes strain on the microsample. A schematic of a dog-bone shape sample typical of tensile specimens is shown in Fig. 7.2.
Microfatigue Testing Systems: The microfatigue systems built based on Sharpe’s initial design contain a piezo actuator capable of generating 0–180 μm of travel with frequencies up to 1000 Hz. The voltage applied to the piezo crystal is proportional to the displacement produced, leading to nanoscale motion. A small button-like load sensor is attached to the free end of the piezo drive, and a gripper is attached to the other side of the load cell. A second gripper is attached to a fixed mount. These grippers have recessed triangular shape areas that house the dog-bone shape end of the microsample. The displacement can be measured in two ways. One way is by recoding the data collected by a displacement monitor built into the piezo drive. The second method is by taking a series of pictures (e.g., a video clip) and analyzing them postmortem. Tests are conducted under load-control using LabVIEW™ (National Instruments Corp., Austin TX) or similar programs. A schematic picture of microfatigue system is presented in Fig. 7.3.
By changing the grippers, small-size CT samples can be tested in fatigue [41]. A typical small CT sample measuring 10 mm × 12 mm × 0.24 mm is shown in Fig. 7.4. The sample holder is in the form of a jacket that completely envelopes the sample except for the pin holes. It also has a small window on one side in its midsection, where the crack is expected to grow. This allows monitoring of the crack tip as it grows during fatigue testing. The jacket is necessary to prevent possible buckling of the thin CT sample.
More recently, a hybrid microtesting system has been developed to combine the functionalities of a microfatigue testing system with that of a microtensile one [42]. The piezo actuator used for nanoscale displacement amplitude of fatigue loading is mounted on a millimeter-scale Uni-slide drive. The latter movement is required for microtensile testing that allows small-size CT specimen characterization. Crack tip travel of this specimen is in the millimeter range (2–4 mm); however, fatigue loading will require displacement amplitudes that are in hundreds of nanometers. LabVIEW programming combined with special functions built into the piezo controller allow uninterrupted testing of the CT specimen (Fig. 7.4).
Microtesting systems have been used to investigate the properties of aluminum foam struts as well as natural fibers [43, 44]. Special fork-like grippers allow mounting Al struts that are cut from open cell aluminum foam block using a ram-type EDM. Strut properties can be incorporated into a mechanics model that predicts the mechanical properties of foam blocks [43, 45]. Local deformation of the struts is measured by image analysis of a series of pictures taken during tensile testing. These show the change in the distance between two landmarks created on the gage section before testing. Natural landmarks on the surface of the struts may also be used to determine the local deformation. Figure 7.6 shows how these landmarks are recognized for determination of their distances throughout the test.
For testing brittle materials in fatigue, a special microfatigue system has been developed [46]. It consists of a capacitively driven comb drive attached to the fatigue specimen. Such a comb drive is shown (see Fig. 7.7) for silicon, measuring about 200 μm × 200 μm. Two interdigitating combs, one attached to the specimen and the other to the substrate, are energized by a sinusoidal voltage wave form at frequencies scaling with the natural frequency of the specimen. For the comb drive shown in Fig. 7.4, a function generator produces a 0–5 V signal that is augmented by an amplifier to 70–140 V and then applied to the interdigitating combs. The specimen with the comb structure constitutes a cantilever with the specimen being at the hinge. The oscillating cantilever will generate enough stresses at the hinge that cause it undergo fatigue and eventually fracture.
The response of the silicon cantilever to the applied voltage is not linear, so there is a need for a calibration curve that allows determination of deformation at various applied voltages. This is achieved by the use of image analyses of pictures obtained at different actuation voltages [46]. The analysis is based on block-matching and ingredient-based method [47–51]. To measure the level of stress at the root of the notch on the specimen, finite element analysis is performed. The elasticity modulus of the structures is usually known by various methods including microtensile testing. Using this known property and knowing the extent of angular displacement (by image analysis), the local stresses can be calculated for different loci on the sample. As an example, for an angular displacement of 1.44°, the local stress changes from 2.74 GPa tensile at the root of the notch to 122 MPa compressive at the back side of the sample (See the location in Fig. 7.7 where the arrow points to) [50].
When this test is conducted under the scanning tip of an AFM raster scanning the surface of the sample, the topography evolution of the surface can be studied. Using this method, the mechanisms of fatigue and fracture of silicon is investigated. Applying FFT transforms of the asperities associated with the roughness near the notch root, certain models can be considered to explain crack initiation from cusps that develop during fatigue of silicon [50].
Direct Loading Methods: Characterization of microsamples has been conducted using small loads, directly applied on specimens. These are usually cantilevers machined out of larger samples. An example is presented in Fig. 7.8, depicting a cantilever beam machined out of Ni-P plate with a thickness of 10 μm. The beam is notched to a depth of 3 μm at a location about 10 μm from the fixed end of the cantilever. The effective length of the beam is 40 μm. The results shown in Fig. 7.8 indicate linear elastic behavior until fracture (e.g., elastic-plastic deformation occurs only at the tip of the notch followed by an abrupt fracture). A Griffith fracture theory analysis can be adopted using Eq. (7.1):
Where σ 0 the tensile stress, c is crack length, and ρ is the radius of the crack tip. The main conclusion of the analysis is that despite plastic deformation at the crack tip, failure is catastrophic [52].
Nanoindentation is another method for characterization of MEMS. One method used to calculate the fracture toughness of thin ceramic films is to measure the crack that initiates and grows upon loading (Fig. 7.9). By knowing the length of the crack, c, the peak load, P, the hardness, H, Young’s modulus, E, and the type of indenter (represented by an empirical number α), the fracture toughness, K 1C can be calculated from Eq. (7.2) [53]:
Cracks are measured from the center of the indent to the end of the crack. An average can be obtained using all cracks initiating from the center of the indent. Cracking of topical brittle materials has been used to measure the creep properties of aluminum thin film sandwiched between the silicon nitride and silicon substrate. In this method, the topical Si3N4 layer is scratched, and the substrate is bent to cause cracks grow. By measuring the crack growth rate, and the load applied in bending the viscosity of the aluminum underlayer is obtained [54].
On-the-Chip Tensile Testing: Efforts have been made to conduct tensile testing on the chips. This is achieved by building the actuator and sensor as well as the test specimen usually on one single chip, manufactured by semiconductor processing. A silicon-on-insulator (SOI) wafer composed of a 35-μm thick p-type device layer, a 2-μm thick buried oxide layer, and a 300-μm thick handle layer was used in one study to develop MEMS tension test device [55]. Deep reactive ion etching (DRIE) process using BOSCH recipe was carried out along with vapor HF acid etching to remove unwanted regions. These included boron oxide and buried silicon dioxide layers, respectively. Tensile test was conducted within scanning electron microscopy using capacitive comb drives to generate force. The force came from many sets of comb-structures electrostatically energized. Capacitive sensors were used for displacement and force measurements. The force is measured by multiplying the elongation of the specimen by the spring constant of the sample beam. Dimensioning of all suspension beams was performed with a scanning electron microscope, SEM. The resulting force and the resulting displacement could be measured with a resolution of 15 nN and 1 nm, respectively.
Nanowires of WC-Co were made using focused ion beam (FIB) microscopy from a bulk WC-Co specimen. The nanowires were then bonded onto the tensile test stage described above using W bonding inside the FIB microscope. Loading of the nanowires was conducted using the capacitive drives until the wires were fractured. Load and displacement was then carefully measured [55] (Fig. 7.9).
4 Modeling of MEMS
Modeling of MEMS devices has been carried out adopting approaches appropriate for their applications. In one such case [56], the nonlinear electromechanical modeling of MEMS switches has been performed. The model takes into account force, damping effects, and position and calculates switching current. It also incorporates changes in the capacitance and voltage with time. The model predicts the switching time, current, velocity, and energy consumed in switching process. It was found out that taking into consideration the damping underneath MEMS bridge makes a large difference in energy and current predicted by this model vs those which ignore such damping.
Modeling software is available to simulate the function of MEMS both mechanically and electrically and characterize their behavior. One such model is COMSOL™ Multiphysics (COSMOL Inc., Burlington, MA). As an example, a silicon pressure sensor can be considered with a silicon membrane that has a cavity underneath isolating it electrically from the ground of the sensor. The pressure of the gas applied to the top pushes the membrane down, thus changing the capacitance between the membrane and the floor. The position of the membrane will be dictated by the pressure on top of it and can be determined from the value of the capacitance. To set up the model, a wizard function built into the simulation software lets the user select 3D space dimensioning. An electromechanics interface is then selected to combine solid mechanics and electrostatics with a moving mesh. This permits the modeling of the motion of the electrostatically actuated structures. There are various options to study, e.g., prestressed analysis, stationary, time dependent, and so on. The stationary study is used when variables do not change with time. It can compute static electric or magnetic fields and direct currents. In solid mechanics, it is used to calculate deformation stresses and strains. In fluid flow, it can determine steady flow and pressure fields. In chemical material transport, it is used to find the steady-state chemical compositions.
Parameters such as pressure, operating temperature, and die-bonding temperature (e.g., 20 kPa, 20 °C, and 70 °C, respectively) are imported from an external file along with geometry parameters. The next step would be to define boundaries (e.g., between the membrane, cavity underneath, and the silicon carbide die). An integrator is used to integrate the point of maximum deflection. Symmetry planes are then defined as xz and yz. There is a steel base to which the sensor is attached. That base will also be defined geometrically. It is the large disk base shown in Fig. 7.10. A cavity domain is then defined and its geometry specified. All components (ignoring the cavity) are defined to be linear elastic solids.
Physics aspects of the models are then specified. These include pressure felt by the membrane, voltage applied to the sensor, and the appropriate boundary conditions. In domains, linear elastic material is selected for all materials except for the vacuum cavity. In boundary selection, symmetry is selected. Symmetry planes are selected on the two vertical walls of the pie shown in Fig. 7.10. At this time, points are defined by selecting prescribed displacement. That prevents the motion of the bottom of the stainless steel base restricting deformation to that depth. In other words, prescribed displacement is constrained within the z-axis. Boundary load condition is defined next. This specifies the pressure that will be applied on the membrane shown by an arrow in Fig. 7.10. Load is defined as pressure and its value is set (e.g., at P 0 = 20 kPa). Mesh boundaries must be selected and the boundaries next to the cavity. Electrostatic boundaries can be entered next. This tells the program about the amount of voltage applied to the underside of the membrane (e.g., 1 V). Following this, ground is selected in boundaries referring to the top of the silicon at the bottom of the cavity.
Materials selection will be performed after specifying boundaries. Silicon with values of 11.7 for relative permittivity, 170 GPa for elasticity modulus, 0.06 for Poisson’s ratio, and 2330 kg/m3 for density. For the cavity, a permittivity of 1 (e.g., vacuum) is entered. Lastly, for the base, Steel AISI 4340 is entered. Corresponding property values will be entered as 7850 kg/m3 for density, 205 GPa for elasticity modulus, 0.28 for the Poisson’s ratio, 1 for relative permittivity, 4.032 × 106 S/m for electrical conductivity, 12.3 × 10−6 for thermal expansion coefficient, and 44.5 W/m K for thermal conductivity. Creating the mesh will come next by selecting a mapped swept mesh with densest to be at the membrane. A size node is selected with a maximum element size of 50 × 10−5 m. The boundary specified by the membrane is defined for this mesh. Mapped meshes are then selected for other parts. It is accomplished by the extension of the fine meshes of the central membrane to the perimeter of the disk. The final step is to sweep the mesh upward all the way to the top of the structure.
Once the geometry, properties, type of the materials, and the size and details of the mesh are configured, the simulation is performed. This involves studies on the application of a range of pressures and analyzing the response of the membrane. The study setting includes adding an auxiliary sweep of appropriate range of pressures with parameters that have a value list of range (0, 5000, 25,000). The computation function is then selected. This creates the map of displacements across the structure (shown as the insert in the pressure–displacement plot of Fig. 7.10). Plots of 1D and 2D can be created by specifying the average vertical displacement (e.g., in μm) and integration of the displacement (e.g., maximum displacement) shown in Fig. 7.10. With this model, the variation of capacitance vs. pressure can be obtained and plotted too. Interestingly, the effect of thermal expansion will also be the change in the capacitance due to thermal stresses. Of course, the coefficient of thermal expansion must also be entered into the model.
The results of the calculations are shown in terms of displacement vs pressure for both cases of presences and absence of thermal stresses. As seen from the plots (7.10), the presence of thermal stresses increase the displacement as well as the capacitance; however, the effect is more pronounced for capacitance at higher pressures. The effect of thermal stresses on the displacement are mapped in the bottom right. There are other simulation tools to characterize MEMS which also predict the behavior of the moving and stationary components and establish performance criteria for the actual device [57, 58].
Mathematical Modeling: Aside from software applications that allow modeling of MEMS components, mathematical modeling is another method adopted by many researchers. One such model is briefly described here [59]. It predicts the static output of the actuation of micromirrors. Consider a mirror plate driven by four Integrated Speed Control, ISC, actuators. The static response of the mirror is established based on the experimental height data obtained at different actuation voltages. The system is considered a 4-input, 4-output model. The actuation of each of the actuators would cause a height change to the corresponding side of the mirror. A 4 × 4 characteristic matrix relates the four actuation voltages as the input and the heights of the mirror as the output. Let character U denote the actuation voltage supplied to the device, the character d represent the resulting displacement, and subscripts specify each of the actuators and each side of the mirror plate. A voltage of 0–3 V is applied to the actual mirror, and the height change is measured by an autofocus microscope with a precision of 0.1 μm. Cubic functions are used to generate accurate fit for the height voltage curves.
Matrix elements are obtained from the coefficients of the four cubic functions established above. Linear superposition of the four sets of equations provide a height voltage matrix. Once the heights effected by applied voltages are calculated with the model, the tilt angles of the mirror plates are formulated as:
Here, W x and W y denote the lengths of the sides of the mirror in x and y directions, and θ x and θ y represent the angles of the mirror plate in x and y axes. The accuracy of the model in predicting the height changes can be inferred from Fig. 7.11, where the predictions are plotted against measured data.
5 Future Trends
The market for MEMS devices is growing rapidly. As an example, the global MEMS market in the area of pressure sensors is going to surpass $4 billion by 2020 [60]. In 2015, the value of this market was about $2 billion. Most of the pressure sensor applications will be automotive, industrial, and healthcare use of which the most dominant is automotive. The total MEMS market was determined to have a value of $8 billion in 2005; however, this number increased to $14 billion in 2015, and furthermore up to $30 billion in 2020 [61]. Of this, about $3.2 billion was in sensors in 2015, and the rest was in inkjet print heads, catheters, and RF IC chips with embedded inductors. The growth of the MEMS market comes not only from the increasing applications of current MEMS such as pressure sensors, triggers for airbags, and other automotive devices, RF MEMS, and miniaturized guidance systems, but also from new MEMS under development. These include disposable chips for performing assays on blood and tissue samples, integrated optical switching and processing chips, RF communication devices, and remote sensing products. Other areas suitable for new MEMS include structural health sensing, as well as detection, analysis, and mitigation of structural damage.
It is postulated that biosensing technologies will be as important in this half century as the microelectronics was to the past half century [62]. Expensive chemical and biological analyses will become inexpensively performed by on-site handheld biochip systems. These have better accuracy and results can be obtained in real time. The smaller size, reduced cost, shorter response time, smaller amount of fluid needed, reduced weight, and other advantages of biochips would radically transform the practice of clinical diagnostics. They make it more efficient and more affordable. It also makes sophisticated analytical techniques available in rural areas, especially developing countries that may lack conventional laboratories. The biochip market is expected to grow to nearly $9.6B in 2016 [62], which is a nearly threefold increase from 2010. It should be remembered that 40 % of the drugs being currently evaluated for clinical trials are transdermal or related to dermal systems. The value for the global transdermal patch market reached $2.8 billion in 2014 [63]. This signifies the importance of microneedles as potential careers for drug delivery of numerous macromolecular drugs for transdermal delivery. The growth in BioMEMS will include microneedles used for transdermal biosensing. The length scale is hundreds of microns and sense analytes such as glucose, biomarkers, and other substances of clinical interest. These microneedles will help develop biochips with end-effectors that interact with biological systems. They also minimize conventional injection-related infections, sample contamination, and analysis artifacts [62].
6 Summary and Concluding Remarks
A brief account of issues related to mechanical properties of MEMS was presented in this chapter. Microtesting techniques including microtensile and microfatigue testing along with the hardware were described with typical sample type, shape, and geometry, depicted with diagrams and images. Modeling MEMS using both computational and mathematical was illustrated by the aid of diagrams and plots. A short passage on future trends completed the chapter.
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The author is grateful to Hadi Allameh for his careful reviewing of the manuscript and for providing helpful suggestions.
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Allameh, S.M. (2017). Mechanical Characterization of MEMS. In: Zhang, D., Wei, B. (eds) Advanced Mechatronics and MEMS Devices II. Microsystems and Nanosystems. Springer, Cham. https://doi.org/10.1007/978-3-319-32180-6_7
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